{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pylab import rcParams\n",
    "import pandas as pd\n",
    "import pylab as pl\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from scipy.cluster.hierarchy import dendrogram, linkage\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cluster import KMeans"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "features = [i for i in range(1,86)]\n",
    "loc = r'/home/sadat/Documents/DSE/Data/HW4_210/Animals_with_Attributes/'\n",
    "predicates = pd.read_csv(loc+'predicates.txt', delimiter='\\t', names=['id','feature'])\n",
    "classes = pd.read_csv(loc+'classes.txt', delimiter='\\t', names=['id','animal'])\n",
    "continuous = pd.read_fwf(loc+'predicate-matrix-continuous.txt', names=features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Analyze the continuous dataset of classes vs features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
       "[5 rows x 85 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "continuous.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perform PCA to decompose from 85 dimensions to 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)\n",
    "pca.fit(continuous.values)\n",
    "X = pca.transform(continuous.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "            0           1\n",
       "0  -14.332003 -106.359925\n",
       "1   58.963086   76.226820\n",
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     "execution_count": 5,
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   ],
   "source": [
    "df = pd.DataFrame(X)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perform K Means of 10 clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('0:', ['antelope', 'horse', 'giraffe', 'zebra', 'deer'], '\\n')\n",
      "('1:', ['german+shepherd', 'tiger', 'leopard', 'fox', 'wolf', 'bobcat', 'lion'], '\\n')\n",
      "('2:', ['killer+whale', 'blue+whale', 'humpback+whale', 'seal', 'walrus', 'dolphin'], '\\n')\n",
      "('3:', ['skunk', 'mole', 'hamster', 'squirrel', 'rabbit', 'rat', 'mouse', 'raccoon'], '\\n')\n",
      "('4:', ['moose', 'ox', 'sheep', 'buffalo', 'giant+panda', 'pig', 'cow'], '\\n')\n",
      "('5:', ['spider+monkey', 'gorilla', 'chimpanzee', 'bat'], '\\n')\n",
      "('6:', ['dalmatian', 'persian+cat', 'siamese+cat', 'chihuahua', 'weasel', 'collie'], '\\n')\n",
      "('7:', ['beaver', 'otter'], '\\n')\n",
      "('8:', ['grizzly+bear', 'polar+bear'], '\\n')\n",
      "('9:', ['hippopotamus', 'elephant', 'rhinoceros'], '\\n')\n"
     ]
    }
   ],
   "source": [
    "km = KMeans(n_clusters=10)\n",
    "km.fit(continuous.values)\n",
    "clusters = km.predict(continuous.values)\n",
    "\n",
    "class_array = classes['animal'].values\n",
    "cluster_dict = {}\n",
    "for i in range(50):\n",
    "    try:\n",
    "        cluster_dict[clusters[i]].append(class_array[i])\n",
    "    except:\n",
    "        cluster_dict[clusters[i]] = []\n",
    "        cluster_dict[clusters[i]].append(class_array[i])\n",
    "\n",
    "for i in range(len(cluster_dict)):\n",
    "    print(str(i)+':',cluster_dict[i],'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perform Hierarchial Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "  [12.5, 12.5, 40.0, 40.0],\n",
       "  [55.0, 55.0, 65.0, 65.0],\n",
       "  [85.0, 85.0, 95.0, 95.0],\n",
       "  [75.0, 75.0, 90.0, 90.0],\n",
       "  [60.0, 60.0, 82.5, 82.5],\n",
       "  [105.0, 105.0, 115.0, 115.0],\n",
       "  [135.0, 135.0, 145.0, 145.0],\n",
       "  [125.0, 125.0, 140.0, 140.0],\n",
       "  [110.0, 110.0, 132.5, 132.5],\n",
       "  [71.25, 71.25, 121.25, 121.25],\n",
       "  [26.25, 26.25, 96.25, 96.25],\n",
       "  [165.0, 165.0, 175.0, 175.0],\n",
       "  [155.0, 155.0, 170.0, 170.0],\n",
       "  [195.0, 195.0, 205.0, 205.0],\n",
       "  [185.0, 185.0, 200.0, 200.0],\n",
       "  [215.0, 215.0, 225.0, 225.0],\n",
       "  [192.5, 192.5, 220.0, 220.0],\n",
       "  [235.0, 235.0, 245.0, 245.0],\n",
       "  [255.0, 255.0, 265.0, 265.0],\n",
       "  [240.0, 240.0, 260.0, 260.0],\n",
       "  [285.0, 285.0, 295.0, 295.0],\n",
       "  [275.0, 275.0, 290.0, 290.0],\n",
       "  [250.0, 250.0, 282.5, 282.5],\n",
       "  [206.25, 206.25, 266.25, 266.25],\n",
       "  [162.5, 162.5, 236.25, 236.25],\n",
       "  [61.25, 61.25, 199.375, 199.375],\n",
       "  [315.0, 315.0, 325.0, 325.0],\n",
       "  [305.0, 305.0, 320.0, 320.0],\n",
       "  [345.0, 345.0, 355.0, 355.0],\n",
       "  [335.0, 335.0, 350.0, 350.0],\n",
       "  [312.5, 312.5, 342.5, 342.5],\n",
       "  [365.0, 365.0, 375.0, 375.0],\n",
       "  [385.0, 385.0, 395.0, 395.0],\n",
       "  [370.0, 370.0, 390.0, 390.0],\n",
       "  [415.0, 415.0, 425.0, 425.0],\n",
       "  [405.0, 405.0, 420.0, 420.0],\n",
       "  [435.0, 435.0, 445.0, 445.0],\n",
       "  [412.5, 412.5, 440.0, 440.0],\n",
       "  [380.0, 380.0, 426.25, 426.25],\n",
       "  [465.0, 465.0, 475.0, 475.0],\n",
       "  [485.0, 485.0, 495.0, 495.0],\n",
       "  [470.0, 470.0, 490.0, 490.0],\n",
       "  [455.0, 455.0, 480.0, 480.0],\n",
       "  [403.125, 403.125, 467.5, 467.5],\n",
       "  [327.5, 327.5, 435.3125, 435.3125],\n",
       "  [130.3125, 130.3125, 381.40625, 381.40625]],\n",
       " 'ivl': ['skunk',\n",
       "  'hamster',\n",
       "  'mouse',\n",
       "  'rabbit',\n",
       "  'giant+panda',\n",
       "  'mole',\n",
       "  'spider+monkey',\n",
       "  'gorilla',\n",
       "  'dalmatian',\n",
       "  'persian+cat',\n",
       "  'chimpanzee',\n",
       "  'squirrel',\n",
       "  'rat',\n",
       "  'chihuahua',\n",
       "  'collie',\n",
       "  'otter',\n",
       "  'beaver',\n",
       "  'polar+bear',\n",
       "  'leopard',\n",
       "  'tiger',\n",
       "  'bobcat',\n",
       "  'fox',\n",
       "  'wolf',\n",
       "  'german+shepherd',\n",
       "  'siamese+cat',\n",
       "  'weasel',\n",
       "  'raccoon',\n",
       "  'lion',\n",
       "  'grizzly+bear',\n",
       "  'bat',\n",
       "  'walrus',\n",
       "  'blue+whale',\n",
       "  'humpback+whale',\n",
       "  'killer+whale',\n",
       "  'seal',\n",
       "  'dolphin',\n",
       "  'antelope',\n",
       "  'horse',\n",
       "  'zebra',\n",
       "  'deer',\n",
       "  'giraffe',\n",
       "  'moose',\n",
       "  'sheep',\n",
       "  'ox',\n",
       "  'cow',\n",
       "  'hippopotamus',\n",
       "  'buffalo',\n",
       "  'pig',\n",
       "  'elephant',\n",
       "  'rhinoceros'],\n",
       " 'leaves': [10,\n",
       "  25,\n",
       "  43,\n",
       "  28,\n",
       "  38,\n",
       "  11,\n",
       "  16,\n",
       "  19,\n",
       "  4,\n",
       "  5,\n",
       "  24,\n",
       "  26,\n",
       "  33,\n",
       "  32,\n",
       "  45,\n",
       "  35,\n",
       "  3,\n",
       "  44,\n",
       "  14,\n",
       "  12,\n",
       "  40,\n",
       "  21,\n",
       "  31,\n",
       "  7,\n",
       "  9,\n",
       "  34,\n",
       "  47,\n",
       "  42,\n",
       "  1,\n",
       "  29,\n",
       "  46,\n",
       "  8,\n",
       "  17,\n",
       "  2,\n",
       "  23,\n",
       "  49,\n",
       "  0,\n",
       "  6,\n",
       "  37,\n",
       "  39,\n",
       "  30,\n",
       "  15,\n",
       "  22,\n",
       "  20,\n",
       "  48,\n",
       "  13,\n",
       "  36,\n",
       "  41,\n",
       "  18,\n",
       "  27]}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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05HvSku9JZb4vLfmetOR70pID0erNrVCmsldomX/3TUmrk3pE1wKmAzMk/VdEPJ3Hfz4F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\nbfuCJPu1Yw9ri+l/K8mx094ZkiRJfTKQgSiwF/D9qtoduI1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Z2MoXJ9myjX5+vqUH/eqw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\nL/5/9wLptgbZGNEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff82c49bc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = linkage(X, 'ward')\n",
    "rcParams[u'figure.figsize'] = [10, 10]\n",
    "plt.title('Hierarchical Clustering Dendrogram', fontsize=15)\n",
    "plt.xlabel('Cluster Distance', fontsize=12)\n",
    "plt.ylabel('Classes', fontsize=12)\n",
    "dendrogram(Z, orientation='right', labels=classes['animal'].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Analyzing the scatter plot for the clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mTYmwVHR77969+vzzz7Vz50794x//UMOGDZWUlCRvb2+tWLHCdlx2draSk5Nt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5fz3//+l/T0dM455xyOO+64SrtfSZL2hz18klQNZWePLQl7/YFbKChI4E9/GgXAhg0b+PDDD2O9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\nDkcccQStW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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7ef9cf610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,15))\n",
    "x = df[0].values\n",
    "y = df[1].values\n",
    "plt.scatter(x,y)\n",
    "for i in range(len(x)):\n",
    "    plt.annotate(classes['animal'].values[i], (x[i],y[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hence, the clustering makes sense if we compare the scatter plot with the dendrogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from struct import unpack\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt \n",
    "\n",
    "def loadmnist(imagefile, labelfile):\n",
    "\n",
    "    # Open the images with gzip in read binary mode\n",
    "    images = open(imagefile, 'rb')\n",
    "    labels = open(labelfile, 'rb')\n",
    "\n",
    "    # Get metadata for images\n",
    "    images.read(4)  # skip the magic_number\n",
    "    number_of_images = images.read(4)\n",
    "    number_of_images = unpack('>I', number_of_images)[0]\n",
    "    rows = images.read(4)\n",
    "    rows = unpack('>I', rows)[0]\n",
    "    cols = images.read(4)\n",
    "    cols = unpack('>I', cols)[0]\n",
    "\n",
    "    # Get metadata for labels\n",
    "    labels.read(4)\n",
    "    N = labels.read(4)\n",
    "    N = unpack('>I', N)[0]\n",
    "\n",
    "    # Get data\n",
    "    x = np.zeros((N, rows*cols), dtype=np.uint8)  # Initialize numpy array\n",
    "    y = np.zeros(N, dtype=np.uint8)  # Initialize numpy array\n",
    "    for i in range(N):\n",
    "        for j in range(rows*cols):\n",
    "            tmp_pixel = images.read(1)  # Just a single byte\n",
    "            tmp_pixel = unpack('>B', tmp_pixel)[0]\n",
    "            x[i][j] = tmp_pixel\n",
    "        tmp_label = labels.read(1)\n",
    "        y[i] = unpack('>B', tmp_label)[0]\n",
    "\n",
    "    images.close()\n",
    "    labels.close()\n",
    "    return (x, y)\n",
    "\n",
    "def displaychar(image):\n",
    "    plt.imshow(np.reshape(image, (28,28)), cmap=plt.cm.gray)\n",
    "    plt.axis('off')\n",
    "    #plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Get file paths\n",
    "path = r'/home/sadat/Documents/DSE/Data/HW3_210/'\n",
    "train_img_path = path + 'train-images.idx3-ubyte'\n",
    "train_lbl_path = path + 'train-labels.idx1-ubyte'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_img, train_lbl = loadmnist(train_img_path, train_lbl_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0</td>\n",
       "      <td>...</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 784 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   0    1    2    3    4    5    6    7    8    9   ...   774  775  776  777  \\\n",
       "0    0    0    0    0    0    0    0    0    0    0 ...     0    0    0    0   \n",
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       "4    0    0    0    0    0    0    0    0    0    0 ...     0    0    0    0   \n",
       "\n",
       "   778  779  780  781  782  783  \n",
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       "\n",
       "[5 rows x 784 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame(train_img)\n",
    "df1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "cov = np.cov(np.transpose(train_img))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 784 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   0    1    2    3    4    5    6    7    8    9   ...   774  775  776  777  \\\n",
       "0    0    0    0    0    0    0    0    0    0    0 ...     0    0    0    0   \n",
       "1    0    0    0    0    0    0    0    0    0    0 ...     0    0    0    0   \n",
       "2    0    0    0    0    0    0    0    0    0    0 ...     0    0    0    0   \n",
       "3    0    0    0    0    0    0    0    0    0    0 ...     0    0    0    0   \n",
       "4    0    0    0    0    0    0    0    0    0    0 ...     0    0    0    0   \n",
       "\n",
       "   778  779  780  781  782  783  \n",
       "0    0    0    0    0    0    0  \n",
       "1    0    0    0    0    0    0  \n",
       "2    0    0    0    0    0    0  \n",
       "3    0    0    0    0    0    0  \n",
       "4    0    0    0    0    0    0  \n",
       "\n",
       "[5 rows x 784 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = pd.DataFrame(cov)\n",
    "df2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eigen_values = np.linalg.eigvals(cov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "denominator = np.sum(eigen_values)\n",
    "\n",
    "def F(k):\n",
    "    numerator = np.sum(eigen_values[k::])\n",
    "    return numerator/denominator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "200:\t0.0335526522989\n",
      "150:\t0.0516435811854\n",
      "100:\t0.0853714275605\n",
      "50:\t0.175353136667\n",
      "25:\t0.3081950912\n"
     ]
    }
   ],
   "source": [
    "k_list = [200, 150, 100, 50, 25]\n",
    "for k in k_list:\n",
    "    print str(k)+':\\t',F(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "_, eigen_vectors = np.linalg.eig(cov)\n",
    "\n",
    "def image_PCA(k, image_id):    \n",
    "    #Take 1000 images to PCA is fast\n",
    "    image = train_img[:1000]\n",
    "    U = eigen_vectors[:,:k]\n",
    "    UUT = np.dot(U,U.T)\n",
    "    image = image.T\n",
    "    X = np.dot(UUT,image).T[image_id]\n",
    "    X = X.reshape(28,28)\n",
    "\n",
    "    #plot \n",
    "    plt.imshow(X, cmap=plt.cm.gray) \n",
    "    plt.title('%i' % k, fontsize = 20)\n",
    "    plt.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VniaTpeAnVWbm59LPESHzbZuMnH7PGZLZZRodmsUZNOmYfk5FjqchY1yiY0b3pL83Od4M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11dTeST5a7e/5z1rzKpIT9a0Hfgpu/vOmsMOePzY6/vbWKuCdmDB9eT7168eBHr6+uxsbEx2TY3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\n/B+b7rkn4nNhnwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efea7cb5e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k_list = [784, 200, 150, 100, 50, 25]\n",
    "index = 0\n",
    "plt.figure(figsize=(15,5))\n",
    "for k in k_list:\n",
    "    index += 1\n",
    "    plt.subplot(1, len(k_list), index)\n",
    "    image_PCA(k,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df1['label'] = train_lbl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_table = {}\n",
    "\n",
    "for i in range(10):\n",
    "    dfn = df1[df1['label']==i].ix[:,0:784]\n",
    "    mat = dfn.values\n",
    "    cov = np.cov(np.transpose(mat))\n",
    "    eigen_values = np.linalg.eigvals(cov)\n",
    "    denominator = np.sum(eigen_values)\n",
    "    val = []\n",
    "    for k in [200, 150, 100, 50, 25]:\n",
    "        numerator = numerator = np.sum(eigen_values[k::])\n",
    "        val.append(np.absolute(numerator/denominator))\n",
    "    F_table[i] = val\n",
    "    F_table['k']= [200, 150, 100, 50, 25]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>0.020961</td>\n",
       "      <td>0.006843</td>\n",
       "      <td>0.028351</td>\n",
       "      <td>0.026279</td>\n",
       "      <td>0.025643</td>\n",
       "      <td>0.023850</td>\n",
       "      <td>0.019147</td>\n",
       "      <td>0.021417</td>\n",
       "      <td>0.025176</td>\n",
       "      <td>0.017133</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>150</th>\n",
       "      <td>0.034483</td>\n",
       "      <td>0.014858</td>\n",
       "      <td>0.046034</td>\n",
       "      <td>0.043591</td>\n",
       "      <td>0.042653</td>\n",
       "      <td>0.040013</td>\n",
       "      <td>0.032732</td>\n",
       "      <td>0.036308</td>\n",
       "      <td>0.043149</td>\n",
       "      <td>0.031092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.059464</td>\n",
       "      <td>0.030986</td>\n",
       "      <td>0.078518</td>\n",
       "      <td>0.076171</td>\n",
       "      <td>0.073684</td>\n",
       "      <td>0.070948</td>\n",
       "      <td>0.057947</td>\n",
       "      <td>0.063601</td>\n",
       "      <td>0.077168</td>\n",
       "      <td>0.057647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>0.119590</td>\n",
       "      <td>0.073012</td>\n",
       "      <td>0.161913</td>\n",
       "      <td>0.159073</td>\n",
       "      <td>0.148018</td>\n",
       "      <td>0.149749</td>\n",
       "      <td>0.122372</td>\n",
       "      <td>0.128934</td>\n",
       "      <td>0.167942</td>\n",
       "      <td>0.123549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.207508</td>\n",
       "      <td>0.131318</td>\n",
       "      <td>0.284332</td>\n",
       "      <td>0.275770</td>\n",
       "      <td>0.253226</td>\n",
       "      <td>0.263515</td>\n",
       "      <td>0.222986</td>\n",
       "      <td>0.222289</td>\n",
       "      <td>0.300042</td>\n",
       "      <td>0.225424</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            0         1         2         3         4         5         6  \\\n",
       "k                                                                           \n",
       "200  0.020961  0.006843  0.028351  0.026279  0.025643  0.023850  0.019147   \n",
       "150  0.034483  0.014858  0.046034  0.043591  0.042653  0.040013  0.032732   \n",
       "100  0.059464  0.030986  0.078518  0.076171  0.073684  0.070948  0.057947   \n",
       "50   0.119590  0.073012  0.161913  0.159073  0.148018  0.149749  0.122372   \n",
       "25   0.207508  0.131318  0.284332  0.275770  0.253226  0.263515  0.222986   \n",
       "\n",
       "            7         8         9  \n",
       "k                                  \n",
       "200  0.021417  0.025176  0.017133  \n",
       "150  0.036308  0.043149  0.031092  \n",
       "100  0.063601  0.077168  0.057647  \n",
       "50   0.128934  0.167942  0.123549  \n",
       "25   0.222289  0.300042  0.225424  "
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_F = pd.DataFrame(F_table)\n",
    "df_F.index=df_F['k']\n",
    "del df_F['k']\n",
    "df_F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Digit with the lowest dimensional projection is 1\n"
     ]
    }
   ],
   "source": [
    "#Convert df back to numpy\n",
    "kfractions = np.array(df_F)\n",
    "\n",
    "#Find the k dimension that has fraction with greatest value\n",
    "k_row = np.argmax(kfractions, axis=0)\n",
    "\n",
    "#With that k value, find the fraction has the lowest value (less lost).\n",
    "amenable_digit = np.argmin(kfractions[k_row[0]], axis=0)\n",
    "\n",
    "print \"Digit with the lowest dimensional projection is\", amenable_digit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
